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    Trigo Graphs Worksheet IB AA SL MATH

    Uploaded by

    Joseph Ang
    This document contains 8 trigonometry problems involving sinusoidal functions of the form f(x) = a sin(bx) or f(x) = a cos(bx). The problems involve identifying amplitude, period, maximum and minimum values, and translating graphs based on given points. Students are asked to find the values of a, b, and other parameters that define the trigonometric functions based on information provided in diagrams of portions of the graphs.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Trigo Graphs Worksheet IB AA SL MATH

    Uploaded by

    Joseph Ang
    191 views5 pages
    This document contains 8 trigonometry problems involving sinusoidal functions of the form f(x) = a sin(bx) or f(x) = a cos(bx). The problems involve identifying amplitude, period, maximum and minimum values, and translating graphs based on given points. Students are asked to find the values of a, b, and other parameters that define the trigonometric functions based on information provided in diagrams of portions of the graphs.

    Original Description:

    Trigonometric graphs worksheet

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    © © All Rights Reserved

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    This document contains 8 trigonometry problems involving sinusoidal functions of the form f(x) = a sin(bx) or f(x) = a cos(bx). The problems involve identifying amplitude, period, maximum and minimum values, and translating graphs based on given points. Students are asked to find the values of a, b, and other parameters that define the trigonometric functions based on information provided in diagrams of portions of the graphs.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    191 views5 pages

    Trigo Graphs Worksheet IB AA SL MATH

    Uploaded by

    Joseph Ang
    This document contains 8 trigonometry problems involving sinusoidal functions of the form f(x) = a sin(bx) or f(x) = a cos(bx). The problems involve identifying amplitude, period, maximum and minimum values, and translating graphs based on given points. Students are asked to find the values of a, b, and other parameters that define the trigonometric functions based on information provided in diagrams of portions of the graphs.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 5

    Trigo Graphs Worksheet

    1. Let 𝑓 𝑥 = 𝑎 sin 𝑏𝑥, for 𝑥 ∈ ℝ. The following diagram shows part of the graph of 𝑓.

    (a) (i) Write down the amplitude of 𝑓.


    (ii) Find the value of 𝑎.

    (b) (i) Write down the period of 𝑓.


    (ii) Find the value of 𝑏.

    2. Let 𝑓 𝑥 = 𝑎 cos 𝑏𝑥, for 𝑥 ∈ ℝ, where 𝑏 > 0. Part of the graph of 𝑓 is shown on the diagram
    below.

    (a) Find the value of 𝑎.


    (b) Find
    (i) the period of 𝑓,
    (ii) the value of 𝑏.

    Page | 1
    3. Let 𝑓 𝑥 = 𝑎 cos 𝑏𝑥 + 𝑑, for 𝑥 ∈ ℝ, where 𝑏 > 0. Part of the graph of 𝑓 is shown on the
    diagram below.

    (a) Find the value of 𝑎.


    (b) (i) Write down the period of 𝑓.
    (ii) Find the value of 𝑏.
    (c) Find the value of 𝑑.

    4. A function is defined by 𝑓 𝑥 = 𝑎 cos 𝑏𝑥 + 𝑑, for 𝑥 ∈ ℝ, where 𝑏 > 0. Part of the graph of 𝑓


    is shown on the diagram below.

    The graph of 𝑓 has a minimum at 𝐴 2, −5 and a maximum at 𝐵 4, 3 . Find the value of

    (a) 𝑎,
    (b) 𝑏,
    (c) 𝑑.

    Page | 2
    5. The following diagram shows the curve 𝑦 = 𝑎 cos 𝑘 𝑥 − 𝑑 + 𝑐 where 𝑎, 𝑘, 𝑑 and 𝑐 are all
    positive constants. The curve has a minimum point at 1.5, 2 and a maximum point 3.5, 7 .

    (a) Write down the values of 𝑎 and 𝑐.


    (b) Find the value of 𝑘.
    (c) Find the smallest possible value of 𝑑, given 𝑑 > 0.

    6. Let 𝑓 𝑥 = 3 sin 𝜋𝑥 + 1.

    (a) Write down the amplitude of 𝑓.


    (b) Find the period of 𝑓.
    (c) On the following grid, sketch the graph of 𝑓, for 0 ≤ 𝑥 ≤ 4.

    Page | 3
    7. Let 𝑓 𝑥 = 𝑝 sin 𝑞𝑥 + 𝑟, for 𝑥 ∈ ℝ. Part of the graph of 𝑓 is shown on the diagram below.

    The graph of 𝑓 has a minimum at 𝐴 3, −1 and a maximum at 𝐵 9, 5 .

    (a) (i) Find the period of 𝑓.


    (ii) Hence, find the value of 𝑞.

    (b) Find the values of

    (i) 𝑝,
    (ii) 𝑟.

    (c) Solve 𝑓 𝑥 = 4, for 0 ≤ 𝑥 ≤ 15.

    𝜋 𝜋
    8. Let 𝑓 𝑥 = sin 𝑥 + 6 + 𝑞. The graph of 𝑓 passes through the point 3
    ,5 .

    (a) Find the value of 𝑞.


    (b) Find the maximum value of 𝑓.
    𝑎
    Let 𝑔 𝑥 = sin 𝑥. The graph of 𝑔 is translated to the graph of 𝑓 by the vector .
    𝑏

    (c) Write down the values of 𝑎 and 𝑏.

    Page | 4
    Answers
    𝜋
    1 (a)(i) Amplitude = 3 (ii) 3 (b)(i) Period = 2
    (ii) 4

    2 (a) 𝑎 = −2 (b)(i) 𝜋 (ii) 𝑏=2

    3 (a) 𝑎=3 (b)(i) 𝜋 (ii) 𝑏=2 (c) 𝑑=1

    𝜋
    4 (a) 𝑎=4 (b) 𝑏= 2
    (c) 𝑑 = −1

    𝜋
    5 (a) 𝑎 = 2.5, 𝑐 = 4.5 (b) 2

    6 (a) 𝑎=3 (b) Period = 2

    (c)

    𝜋
    7 (a)(i) Period = 12 (ii) 𝑞= 6
    (b)(i) 𝑝 = −3 (ii) 𝑟=2
    (c) 𝑥 = 7.39, 10.6

    𝜋
    8 (a) 𝑞=4 (b) 5 (c) 𝑎 = − 6, 𝑏 = 4

    Page | 5

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